Solve f=1-x/x-2

$$f = \frac{ 1-x }{ x-2 }$$

Solve for x

$$x=\frac{2f+1}{f+1}$$

$$f\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$f\left(x-2\right)=1-x$$

Use the distributive property to multiply f by x-2.

$$fx-2f=1-x$$

Add x to both sides.

$$fx-2f+x=1$$

Add 2f to both sides.

$$fx+x=1+2f$$

Combine all terms containing x.

$$\left(f+1\right)x=1+2f$$

The equation is in standard form.

$$\left(f+1\right)x=2f+1$$

Divide both sides by f+1.

$$\frac{\left(f+1\right)x}{f+1}=\frac{2f+1}{f+1}$$

Dividing by f+1 undoes the multiplication by f+1.

$$x=\frac{2f+1}{f+1}$$

Variable x cannot be equal to 2.

$$x=\frac{2f+1}{f+1}\text{, }x\neq 2$$

Solve for f

$$f=-\frac{x-1}{x-2}$$

$$x\neq 2$$